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If 3x-y=12, what is the value of

8x

2y

?

A) 212

B) 44

C) 82

D) The value cannot be determined from the information given.

Answer: One approach is to express

8x

2y

so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 23 for 8 in the numerator of

8x

2y

gives

(23) x

2y

which can be rewritten

23x

2y

Since the numerator and denominator of have a common base, this expression can be rewritten as 2 (3x-y). In the question, it states that 3x-y=12, so one can substitute 12 for the exponent, 3x-y, which means that

8x

2y

=212

The final answer is A.